It is unlikely that you can obtain an Illinois driver's license while your Virginia license is still suspended. Normally you would need to reinstate your VA license so that IL will allow you to apply for driver's license.

All states look at the National Driver Register (NDR) which lists "problem drivers" meaning those with serious offenses, such as DUIs on their record and motorists who have their license cancelled, revoked or suspended.

The Illinois Secretary of State states that drivers moving to Illinois may use their valid driver's license from their home state or country for 90 days. You may obtain an Illinois driver's license or identification card only if you are becoming a legal resident of Illinois.

If you have a valid driver's license from another state or country, you may use it to drive in Illinois throughout your stay (if you do not plan to become a permanent resident of this state). Illinois does not recognize the international driver's license.

Illinois drivers whose driving privileges have been revoked or suspended may be allowed to drive using special restricted permits so you may want to see if it is possible to apply for this while taking care of your issues in VA. The IL SOS will be able to tell you for certain if you can obtain an Illinois driver's license if you contact them and discuss your specific situation.